A Lower Bound for a Class of Graph Based Loss-resilient Codes Work of Both Authors Has Been Supported by Grant 21-49626.96 from Schweizer Nation- Alfonds (snf)

Recently, Luby et al. constructed information-theoretically almost optimal loss-resilient codes. The construction is based on a sequence of bipartite graphs. Using a probabilistic construction for the individual bipartite graphs, they obtain loss-resilient codes that have very eecient encoding and decoding algorithms. They left open the question whether there are other bipartite graphs leading to codes with even more eecient encoding and decoding algorithms. In this paper we show that if one follows the basic construction used by Luby et al., then their choice of bipartite graphs leads to codes with asymptotically optimal encoding and decoding algorithms.